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過去の記録
過去の記録 ～10/09｜本日 10/10 | 今後の予定 10/11～
2013年11月14日(木)
幾何コロキウム
10:00-11:30 数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
梶浦宏成 氏 (千葉大学)
トーラスファイバー束のホモロジー的ミラー対称性とその変形 (JAPANESE)
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
梶浦宏成 氏 (千葉大学)
トーラスファイバー束のホモロジー的ミラー対称性とその変形 (JAPANESE)
[ 講演概要 ]
Strominger-Yau-Zaslow によるトーラスファイバー束によるミラー対称性の定式化のある変形として, ある葉層構造を持つシンプレクティックトーラスファイバー束と複素トーラスファイバー束のある非可換変形の組を考える. この変形の組がミラー双対であると主張するための根拠として, 両者の間のホモロジー的ミラー対称性を考える. つまり, シンプレクティックトーラスファイバー束上の深谷圏と複素トーラスファイバー束上の連接層の導来圏の変形を考え, その2つの圏の同値性について議論する. (変形していない状況で分かっているレベルで, その変形した設定でも成り立つことがいえる. )
Strominger-Yau-Zaslow によるトーラスファイバー束によるミラー対称性の定式化のある変形として, ある葉層構造を持つシンプレクティックトーラスファイバー束と複素トーラスファイバー束のある非可換変形の組を考える. この変形の組がミラー双対であると主張するための根拠として, 両者の間のホモロジー的ミラー対称性を考える. つまり, シンプレクティックトーラスファイバー束上の深谷圏と複素トーラスファイバー束上の連接層の導来圏の変形を考え, その2つの圏の同値性について議論する. (変形していない状況で分かっているレベルで, その変形した設定でも成り立つことがいえる. )
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
Danielle Hilhorst 氏 (Université de Paris-Sud / CNRS)
Singular limit of a damped wave equation with a bistable nonlinearity (ENGLISH)
Danielle Hilhorst 氏 (Université de Paris-Sud / CNRS)
Singular limit of a damped wave equation with a bistable nonlinearity (ENGLISH)
[ 講演概要 ]
We study the singular limit of a damped wave equation with
a bistable nonlinearity. In order to understand interfacial
phenomena, we derive estimates for the generation and the motion
of interfaces. We prove that steep interfaces are generated in
a short time and that their motion is governed by mean curvature
flow under the assumption that the damping is sufficiently strong.
To this purpose, we prove a comparison principle for the damped
wave equation and construct suitable sub- and super-solutions.
This is joint work with Mitsunori Nata.
We study the singular limit of a damped wave equation with
a bistable nonlinearity. In order to understand interfacial
phenomena, we derive estimates for the generation and the motion
of interfaces. We prove that steep interfaces are generated in
a short time and that their motion is governed by mean curvature
flow under the assumption that the damping is sufficiently strong.
To this purpose, we prove a comparison principle for the damped
wave equation and construct suitable sub- and super-solutions.
This is joint work with Mitsunori Nata.
2013年11月13日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Mark Wilkinson 氏 (École normale supérieure - Paris)
Eigenvalue Constraints and Regularity of Q-tensor Navier-Stokes Dynamics (ENGLISH)
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Mark Wilkinson 氏 (École normale supérieure - Paris)
Eigenvalue Constraints and Regularity of Q-tensor Navier-Stokes Dynamics (ENGLISH)
[ 講演概要 ]
The Q-tensor is a traceless and symmetric 3x3 matrix that describes the small-scale structure in nematic liquid crystals. In order to be physically meaningful, its eigenvalues should be bounded below by -1/3 and above by 2/3. This constraint raises questions regarding the physical predictions of theories which employ the Q-tensor; it also raises analytical issues in both static and dynamic Q-tensor theories of nematic liquid crystals. John Ball and Apala Majumdar recently constructed a singular map on traceless, symmetric matrices that penalises unphysical Q-tensors by giving them an infinite energy cost. In this talk, I shall present some mathematical results for a coupled Navier-Stokes system modelling nematic dynamics into which this map is built, including the existence, regularity and so-called `strict physicality' of its weak solutions.
The Q-tensor is a traceless and symmetric 3x3 matrix that describes the small-scale structure in nematic liquid crystals. In order to be physically meaningful, its eigenvalues should be bounded below by -1/3 and above by 2/3. This constraint raises questions regarding the physical predictions of theories which employ the Q-tensor; it also raises analytical issues in both static and dynamic Q-tensor theories of nematic liquid crystals. John Ball and Apala Majumdar recently constructed a singular map on traceless, symmetric matrices that penalises unphysical Q-tensors by giving them an infinite energy cost. In this talk, I shall present some mathematical results for a coupled Navier-Stokes system modelling nematic dynamics into which this map is built, including the existence, regularity and so-called `strict physicality' of its weak solutions.
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 056号室
Yichao Tian 氏 (Morningside Center for Mathematics)
Goren-Oort stratification and Tate cycles on Hilbert modular varieties (ENGLISH)
Yichao Tian 氏 (Morningside Center for Mathematics)
Goren-Oort stratification and Tate cycles on Hilbert modular varieties (ENGLISH)
[ 講演概要 ]
Let B be a quaternionic algebra over a totally real field F, and p be a prime at least 3 unramified in F. We consider a Shimura variety X associated to B^* of level prime to p. A generalization of Deligne-Carayol's "modèle étrange" allows us to define an integral model for X. We will then define a Goren-Oort stratification on the characteristic p fiber of X, and show that each closed Goren-Oort stratum is an iterated P^1-fibration over another quaternionic Shimura variety in characteristic p. Now suppose that [F:Q] is even and that p is inert in F. An iteration of this construction gives rise to many algebraic cycles of middle codimension on the characteristic p fibre of Hilbert modular varieties of prime-to-p level. We show that the cohomological classes of these cycles generate a large subspace of the Tate cycles, which, in some special cases, coincides with the prediction of the Tate conjecture for the Hilbert modular variety over finite fields. This is a joint work with Liang Xiao.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
Let B be a quaternionic algebra over a totally real field F, and p be a prime at least 3 unramified in F. We consider a Shimura variety X associated to B^* of level prime to p. A generalization of Deligne-Carayol's "modèle étrange" allows us to define an integral model for X. We will then define a Goren-Oort stratification on the characteristic p fiber of X, and show that each closed Goren-Oort stratum is an iterated P^1-fibration over another quaternionic Shimura variety in characteristic p. Now suppose that [F:Q] is even and that p is inert in F. An iteration of this construction gives rise to many algebraic cycles of middle codimension on the characteristic p fibre of Hilbert modular varieties of prime-to-p level. We show that the cohomological classes of these cycles generate a large subspace of the Tate cycles, which, in some special cases, coincides with the prediction of the Tate conjecture for the Hilbert modular variety over finite fields. This is a joint work with Liang Xiao.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 118号室
Issan Patri 氏 (Inst. Math. Sci.)
Automorphisms of Compact Quantum Groups (ENGLISH)
Issan Patri 氏 (Inst. Math. Sci.)
Automorphisms of Compact Quantum Groups (ENGLISH)
2013年11月12日(火)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Reinhard Farwig 氏 (Technische Universität Darmstadt)
Optimal initial values and regularity conditions of Besov space type for weak solutions to the Navier-Stokes system (ENGLISH)
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Reinhard Farwig 氏 (Technische Universität Darmstadt)
Optimal initial values and regularity conditions of Besov space type for weak solutions to the Navier-Stokes system (ENGLISH)
[ 講演概要 ]
In a joint work with H. Sohr (Paderborn) and W. Varnhorn (Kassel) we discuss the optimal condition on initial values for the instationary Navier-Stokes system in a bounded domain to get a locally regular solution in Serrin's class.
Then this result based on a description in Besov spaces will be used at all or almost all instants to prove new conditional regularity results for weak solutions.
In a joint work with H. Sohr (Paderborn) and W. Varnhorn (Kassel) we discuss the optimal condition on initial values for the instationary Navier-Stokes system in a bounded domain to get a locally regular solution in Serrin's class.
Then this result based on a description in Besov spaces will be used at all or almost all instants to prove new conditional regularity results for weak solutions.
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Alexander Voronov 氏 (University of Minnesota)
The Batalin-Vilkovisky Formalism and Cohomology of Moduli Spaces (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Alexander Voronov 氏 (University of Minnesota)
The Batalin-Vilkovisky Formalism and Cohomology of Moduli Spaces (ENGLISH)
[ 講演概要 ]
We use the Batalin-Vilkovisky formalism to give a new proof of Costello's theorem on the existence and uniqueness of solution to the Quantum Master Equation. We also make a physically motivated conjecture on the rational homology of moduli spaces. This is a joint work with Domenico D'Alessandro.
We use the Batalin-Vilkovisky formalism to give a new proof of Costello's theorem on the existence and uniqueness of solution to the Quantum Master Equation. We also make a physically motivated conjecture on the rational homology of moduli spaces. This is a joint work with Domenico D'Alessandro.
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
http://www.infsup.jp/utnas/
柏原崇人 氏 (東京大学大学院数理科学研究科)
``method of numerical integration''による摩擦型境界条件問題の数値解析について (JAPANESE)
http://www.infsup.jp/utnas/
http://www.infsup.jp/utnas/
柏原崇人 氏 (東京大学大学院数理科学研究科)
``method of numerical integration''による摩擦型境界条件問題の数値解析について (JAPANESE)
[ 講演概要 ]
摩擦型境界条件を課したStokes方程式(もしくはPoisson方程式・線形弾性体方程式)の数値解析を紹介する.摩擦型境界条件問題は,非線形項が境界上のL1ノルムで表される楕円型変分不等式として定式化される.本研究では,この非線形項を適切な数値積分公式で近似した有限要素スキームを提案する.そのような数値積分近似の導入により,(i)変分不等式が方程式に書き換えられること,(ii)相補性条件,というPDEのレベルで成り立つ2つの性質が離散化後も保たれることを示す.さらに,離散版の相補性条件にもとづいた実装法(Active/Inactive集合法)を提案し,その有効性を数値実験で確かめる.時間があればSignorini境界条件・多角形以外の領域・時間非定常問題への応用についても紹介したい.
[ 参考URL ]摩擦型境界条件を課したStokes方程式(もしくはPoisson方程式・線形弾性体方程式)の数値解析を紹介する.摩擦型境界条件問題は,非線形項が境界上のL1ノルムで表される楕円型変分不等式として定式化される.本研究では,この非線形項を適切な数値積分公式で近似した有限要素スキームを提案する.そのような数値積分近似の導入により,(i)変分不等式が方程式に書き換えられること,(ii)相補性条件,というPDEのレベルで成り立つ2つの性質が離散化後も保たれることを示す.さらに,離散版の相補性条件にもとづいた実装法(Active/Inactive集合法)を提案し,その有効性を数値実験で確かめる.時間があればSignorini境界条件・多角形以外の領域・時間非定常問題への応用についても紹介したい.
http://www.infsup.jp/utnas/
2013年11月11日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
足立 真訓 氏 (名古屋大学)
Levi-flat real hypersurfaces with Takeuchi 1-complete complements (JAPANESE)
足立 真訓 氏 (名古屋大学)
Levi-flat real hypersurfaces with Takeuchi 1-complete complements (JAPANESE)
[ 講演概要 ]
In this talk, we discuss compact Levi-flat real hypersurfaces with Takeuchi 1-complete complements from several viewpoints. Based on a Bochner-Hartogs type extension theorem for CR sections over these hypersurfaces, we give an example of a compact Levi-flat CR manifold with a positive CR line bundle whose Ohsawa-Sibony's projective embedding map cannot be transversely infinitely differentiable. We also give a geometrical expression of the Diederich-Fornaess exponents of Takeuchi 1-complete defining functions, and discuss a possible dynamical interpretation of them.
In this talk, we discuss compact Levi-flat real hypersurfaces with Takeuchi 1-complete complements from several viewpoints. Based on a Bochner-Hartogs type extension theorem for CR sections over these hypersurfaces, we give an example of a compact Levi-flat CR manifold with a positive CR line bundle whose Ohsawa-Sibony's projective embedding map cannot be transversely infinitely differentiable. We also give a geometrical expression of the Diederich-Fornaess exponents of Takeuchi 1-complete defining functions, and discuss a possible dynamical interpretation of them.
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
Sung Rak Choi 氏 (POSTECH)
Geography via the base loci (ENGLISH)
Sung Rak Choi 氏 (POSTECH)
Geography via the base loci (ENGLISH)
[ 講演概要 ]
The geography of log model refers to the decomposition of the set of effective adjoint divisors into the cells defined by the resulting models that are obtained by the log minimal model program.
We will describe the geography in terms of the asymptotic base loci and Zariski decompositions of divisors.
As an application, we give a partial answer to a question of B. Totaro concerning the structure of partially ample cones.
The geography of log model refers to the decomposition of the set of effective adjoint divisors into the cells defined by the resulting models that are obtained by the log minimal model program.
We will describe the geography in terms of the asymptotic base loci and Zariski decompositions of divisors.
As an application, we give a partial answer to a question of B. Totaro concerning the structure of partially ample cones.
Lie群論・表現論セミナー
16:30-17:30 数理科学研究科棟(駒場) 126号室
Ronald King 氏 (the University of Southampton)
Alternating sign matrices, primed shifted tableaux and Tokuyama
factorisation theorems (ENGLISH)
Ronald King 氏 (the University of Southampton)
Alternating sign matrices, primed shifted tableaux and Tokuyama
factorisation theorems (ENGLISH)
[ 講演概要 ]
Twenty years ago Okada established a remarkable set of identities relating weighted sums over half-turn alternating sign matrices (ASMs) to products taking the form of deformations of Weyl denominator formulae for Lie algebras B_n, C_n and D_n. Shortly afterwards Simpson added another such identity to the list. It will be shown that various classes of ASMs are in bijective correspondence with certain sets of shifted tableaux, and that statistics on these ASMs may be expressed in terms of the entries in corresponding compass point matrices (CPMs). This then enables the Okada and Simpson identities to be expressed in terms of weighted sums over primed shifted tableaux. This offers the possibility of extending each of these identities, that originally involved a single parameter and a single shifted tableau shape, to more general identities involving both sequences of parameters and shapes specified by arbitrary partitions. It is conjectured that in each case an appropriate multi-parameter weighted sum can be expressed as a product of a deformed Weyl denominator and group character of the type first proved in the A_n case by Tokuyma in 1988. The conjectured forms of the generalised Okada and Simpson identities will be given explicitly, along with an account of recent progress made in collaboration with Angèle Hamel in proving some of them.
Twenty years ago Okada established a remarkable set of identities relating weighted sums over half-turn alternating sign matrices (ASMs) to products taking the form of deformations of Weyl denominator formulae for Lie algebras B_n, C_n and D_n. Shortly afterwards Simpson added another such identity to the list. It will be shown that various classes of ASMs are in bijective correspondence with certain sets of shifted tableaux, and that statistics on these ASMs may be expressed in terms of the entries in corresponding compass point matrices (CPMs). This then enables the Okada and Simpson identities to be expressed in terms of weighted sums over primed shifted tableaux. This offers the possibility of extending each of these identities, that originally involved a single parameter and a single shifted tableau shape, to more general identities involving both sequences of parameters and shapes specified by arbitrary partitions. It is conjectured that in each case an appropriate multi-parameter weighted sum can be expressed as a product of a deformed Weyl denominator and group character of the type first proved in the A_n case by Tokuyma in 1988. The conjectured forms of the generalised Okada and Simpson identities will be given explicitly, along with an account of recent progress made in collaboration with Angèle Hamel in proving some of them.
統計数学セミナー
14:50-16:00 数理科学研究科棟(駒場) 052号室
二宮 嘉行 氏 (九州大学)
LASSO に対する AIC タイプの情報量規準 (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/06.html
二宮 嘉行 氏 (九州大学)
LASSO に対する AIC タイプの情報量規準 (JAPANESE)
[ 講演概要 ]
LASSO は L1 罰則項を推定関数の中に入れる正則化法であり,その開発・拡張は統計科学や機械学習といった分野のホットトピックの一つとなっている.本講演では,罰則項にかかる係数,つまり罰則の強弱を決めるチューニングパラメータの選択問題を考える.クロスバリデーションやサブサンプリングで選択する方法が広く用いられているが,基本的にそれらは計算負荷が高い.そこで,Zou et al. (2007) の「AIC for the LASSO」を拡張する形の情報量規準の導出を試みる.
本講演は阪大で開催し,東大数理へウェブ配信いたします.
[ 参考URL ]LASSO は L1 罰則項を推定関数の中に入れる正則化法であり,その開発・拡張は統計科学や機械学習といった分野のホットトピックの一つとなっている.本講演では,罰則項にかかる係数,つまり罰則の強弱を決めるチューニングパラメータの選択問題を考える.クロスバリデーションやサブサンプリングで選択する方法が広く用いられているが,基本的にそれらは計算負荷が高い.そこで,Zou et al. (2007) の「AIC for the LASSO」を拡張する形の情報量規準の導出を試みる.
本講演は阪大で開催し,東大数理へウェブ配信いたします.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/06.html
2013年11月08日(金)
作用素環セミナー
10:00-12:00 数理科学研究科棟(駒場) 122号室
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory IV (JAPANESE)
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory IV (JAPANESE)
談話会・数理科学講演会
16:30-17:30 数理科学研究科棟(駒場) 123号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Dipendra Prasad 氏 (Tata Institute of Fundamental Research)
Ext Analogues of Branching laws (ENGLISH)
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Dipendra Prasad 氏 (Tata Institute of Fundamental Research)
Ext Analogues of Branching laws (ENGLISH)
[ 講演概要 ]
The decomposition of a representation of a group when restricted to a
subgroup is an important problem well-studied for finite and compact Lie
groups, and continues to be of much contemporary interest in the context
of real and $p$-adic groups. We will survey some of the questions that have
recently been considered, and look at a variation of these questions involving concepts in homological algebra which gives rise to interesting newer questions.
The decomposition of a representation of a group when restricted to a
subgroup is an important problem well-studied for finite and compact Lie
groups, and continues to be of much contemporary interest in the context
of real and $p$-adic groups. We will survey some of the questions that have
recently been considered, and look at a variation of these questions involving concepts in homological algebra which gives rise to interesting newer questions.
2013年11月07日(木)
作用素環セミナー
15:30-17:30 数理科学研究科棟(駒場) 123号室
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory III (JAPANESE)
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory III (JAPANESE)
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 370号室
Bingyu Zhang 氏 (University of Cincinnati)
Maximum Regularity Principle for Conservative Evolutionary Partial Di erential Equations (ENGLISH)
Bingyu Zhang 氏 (University of Cincinnati)
Maximum Regularity Principle for Conservative Evolutionary Partial Di erential Equations (ENGLISH)
Lie群論・表現論セミナー
13:30-14:20 数理科学研究科棟(駒場) 000号室
小林俊行 氏 (東京大学大学院数理科学研究科)
擬リーマン局所等質空間上の大域幾何と解析 (ENGLISH)
小林俊行 氏 (東京大学大学院数理科学研究科)
擬リーマン局所等質空間上の大域幾何と解析 (ENGLISH)
[ 講演概要 ]
The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry of general signature, surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.
Taking anti-de Sitter manifolds, which are locally modelled on AdS^n as an example, I plan to explain two programs:
1. (global shape) Exisitence problem of compact locally homogeneous spaces, and defomation theory.
2. (spectral analysis) Construction of the spectrum of the Laplacian, and its stability under the deformation of the geometric structure.
The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry of general signature, surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.
Taking anti-de Sitter manifolds, which are locally modelled on AdS^n as an example, I plan to explain two programs:
1. (global shape) Exisitence problem of compact locally homogeneous spaces, and defomation theory.
2. (spectral analysis) Construction of the spectrum of the Laplacian, and its stability under the deformation of the geometric structure.
Lie群論・表現論セミナー
14:30-17:40 数理科学研究科棟(駒場) 000号室
Vaibhav Vaish 氏 (the Institute of Mathematical Sciences) 14:30-15:20
Weightless cohomology of algebraic varieties (ENGLISH)
Visible actions on generalized flag varieties
--- Geometry of multiplicity-free representations of $SO(N)$ (ENGLISH)
Holomorphic discrete series and Borel-de Siebenthal discrete series (ENGLISH)
Branching laws and the local Langlands correspondence (ENGLISH)
Vaibhav Vaish 氏 (the Institute of Mathematical Sciences) 14:30-15:20
Weightless cohomology of algebraic varieties (ENGLISH)
[ 講演概要 ]
Using Morel's weight truncations in categories of mixed sheaves, we attach to any variety defined over complex numbers, over finite fields or even over a number field, a series of groups called the weightless cohomology groups. These lie between the usual cohomology and the intersection cohomology, have a natural ring structure, satisfy Kunneth, and are functorial for certain morphisms.
The construction is motivic and naturally arises in the context of Shimura Varieties where they capture the cohomology of Reductive Borel-Serre compactification. The construction also yields invariants of singularities associated with the combinatorics of the boundary divisors in any resolution.
Yuichiro Tanaka 氏 (the University of Tokyo) 15:40-16:10Using Morel's weight truncations in categories of mixed sheaves, we attach to any variety defined over complex numbers, over finite fields or even over a number field, a series of groups called the weightless cohomology groups. These lie between the usual cohomology and the intersection cohomology, have a natural ring structure, satisfy Kunneth, and are functorial for certain morphisms.
The construction is motivic and naturally arises in the context of Shimura Varieties where they capture the cohomology of Reductive Borel-Serre compactification. The construction also yields invariants of singularities associated with the combinatorics of the boundary divisors in any resolution.
Visible actions on generalized flag varieties
--- Geometry of multiplicity-free representations of $SO(N)$ (ENGLISH)
[ 講演概要 ]
The subject of study is tensor product representations of irreducible representations of the orthogonal group, which are multiplicity-free. Here we say a group representation is multiplicity-free if any irreducible representation occurs at most once in its irreducible decomposition.
The motivation is the theory of visible actions on complex manifolds, which was introduced by T. Kobayashi. In this theory, the main tool for proving the multiplicity-freeness property of group representations is the ``propagation theorem of the multiplicity-freeness property". By using this theorem and Stembridge's classification result, we obtain the following: All the multiplicity-free tensor product representations of $SO(N)$ and $Spin(N)$ can be obtained from character, alternating tensor product and spin representations combined with visible actions on orthogonal generalized flag varieties.
Pampa Paul 氏 (Indian Statistical Institute, Kolkata) 16:10-16:40The subject of study is tensor product representations of irreducible representations of the orthogonal group, which are multiplicity-free. Here we say a group representation is multiplicity-free if any irreducible representation occurs at most once in its irreducible decomposition.
The motivation is the theory of visible actions on complex manifolds, which was introduced by T. Kobayashi. In this theory, the main tool for proving the multiplicity-freeness property of group representations is the ``propagation theorem of the multiplicity-freeness property". By using this theorem and Stembridge's classification result, we obtain the following: All the multiplicity-free tensor product representations of $SO(N)$ and $Spin(N)$ can be obtained from character, alternating tensor product and spin representations combined with visible actions on orthogonal generalized flag varieties.
Holomorphic discrete series and Borel-de Siebenthal discrete series (ENGLISH)
[ 講演概要 ]
Let $G_0$ be a simply connected non-compact real simple Lie group with maximal compact subgroup $K_0$.
Let $T_0\\subset K_0$ be a Cartan subgroup of $K_0$ as well as of $G_0$. So $G_0$ has discrete series representations.
Denote by $\\frak{g}, \\frak{k},$ and $\\frak{t}$, the
complexifications of the Lie algebras $\\frak{g}_0, \\frak{k}_0$ and $\\frak{t}_0$ of $G_0, K_0$ and $T_0$ respectively.
There exists a positive root system $\\Delta^+$ of $\\frak{g}$ with respect to $\\frak{t}$, known as the Borel-de Siebenthal positive system for which there is exactly one non-compact simple root, denoted $\\nu$. Let $\\mu$ denote the highest root.
If $G_0/K_0$ is Hermitian symmetric, then $\\nu$ has coefficient $1$ in $\\mu$ and one can define holomorphic discrete series representation of $G_0$ using $\\Delta^+$.
If $G_0/K_0$ is not Hermitian symmetric, the coefficient of $\\nu$ in the highest root $\\mu$ is $2$.
In this case, Borel-de Siebenthal discrete series of $G_0$ is defined using $\\Delta^+$ in a manner analogous to the holomorphic discrete series.
Let $\\nu^*$ be the fundamental weight corresponding to $\\nu$ and $L_0$ be the centralizer in $K_0$ of the circle subgroup defined by $i\\nu^*$.
Note that $L_0 = K_0$, when $G_0/K_0$ is Hermitian symmetric. Otherwise, $L_0$ is a proper subgroup of $K_0$ and $K_0/L_0$ is an irreducible compact Hermitian symmetric space.
Let $G$ be the simply connected Lie group with Lie algebra $\\frak{g}$ and $K_0^* \\subset G$ be the dual of $K_0$ with respect to $L_0$ (or, the image of $L_0$ in $G$).
Then $K_0^*/L_0$ is an irreducible non-compact Hermitian symmetric space dual to $K_0/L_0$.
In this talk, to each Borel-de Siebenthal discrete series of $G_0$, a holomorphic discrete series of $K_0^*$ will be associated and occurrence of common $L_0$-types in both the series will be discussed.
Dipendra Prasad 氏 (Tata Institute of Fundamental Research) 16:50-17:40Let $G_0$ be a simply connected non-compact real simple Lie group with maximal compact subgroup $K_0$.
Let $T_0\\subset K_0$ be a Cartan subgroup of $K_0$ as well as of $G_0$. So $G_0$ has discrete series representations.
Denote by $\\frak{g}, \\frak{k},$ and $\\frak{t}$, the
complexifications of the Lie algebras $\\frak{g}_0, \\frak{k}_0$ and $\\frak{t}_0$ of $G_0, K_0$ and $T_0$ respectively.
There exists a positive root system $\\Delta^+$ of $\\frak{g}$ with respect to $\\frak{t}$, known as the Borel-de Siebenthal positive system for which there is exactly one non-compact simple root, denoted $\\nu$. Let $\\mu$ denote the highest root.
If $G_0/K_0$ is Hermitian symmetric, then $\\nu$ has coefficient $1$ in $\\mu$ and one can define holomorphic discrete series representation of $G_0$ using $\\Delta^+$.
If $G_0/K_0$ is not Hermitian symmetric, the coefficient of $\\nu$ in the highest root $\\mu$ is $2$.
In this case, Borel-de Siebenthal discrete series of $G_0$ is defined using $\\Delta^+$ in a manner analogous to the holomorphic discrete series.
Let $\\nu^*$ be the fundamental weight corresponding to $\\nu$ and $L_0$ be the centralizer in $K_0$ of the circle subgroup defined by $i\\nu^*$.
Note that $L_0 = K_0$, when $G_0/K_0$ is Hermitian symmetric. Otherwise, $L_0$ is a proper subgroup of $K_0$ and $K_0/L_0$ is an irreducible compact Hermitian symmetric space.
Let $G$ be the simply connected Lie group with Lie algebra $\\frak{g}$ and $K_0^* \\subset G$ be the dual of $K_0$ with respect to $L_0$ (or, the image of $L_0$ in $G$).
Then $K_0^*/L_0$ is an irreducible non-compact Hermitian symmetric space dual to $K_0/L_0$.
In this talk, to each Borel-de Siebenthal discrete series of $G_0$, a holomorphic discrete series of $K_0^*$ will be associated and occurrence of common $L_0$-types in both the series will be discussed.
Branching laws and the local Langlands correspondence (ENGLISH)
[ 講演概要 ]
The decomposition of a representation of a group when restricted to a subgroup is an important problem well-studied for finite and compact Lie groups, and continues to be of much contemporary interest in the context of real and $p$-adic groups. We will survey some of the questions that have recently been considered drawing analogy with Compact Lie groups, and what it suggests in the context of real and $p$-adic groups via what is called the local Langlands correspondence.
The decomposition of a representation of a group when restricted to a subgroup is an important problem well-studied for finite and compact Lie groups, and continues to be of much contemporary interest in the context of real and $p$-adic groups. We will survey some of the questions that have recently been considered drawing analogy with Compact Lie groups, and what it suggests in the context of real and $p$-adic groups via what is called the local Langlands correspondence.
2013年11月06日(水)
作用素環セミナー
10:00-12:00 数理科学研究科棟(駒場) 122号室
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory II (JAPANESE)
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory II (JAPANESE)
2013年11月05日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 123号室
Tea: 16:00 - 16:30 コモンルーム
Carlos Moraga Ferrandiz 氏 (東京大学大学院数理科学研究科, 日本学術振興会)
The isotopy problem of non-singular closed 1-forms. (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Carlos Moraga Ferrandiz 氏 (東京大学大学院数理科学研究科, 日本学術振興会)
The isotopy problem of non-singular closed 1-forms. (ENGLISH)
[ 講演概要 ]
Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class.
A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.
The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.
Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class.
A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.
The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.
作用素環セミナー
15:30-17:30 数理科学研究科棟(駒場) 118号室
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory I (JAPANESE)
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory I (JAPANESE)
2013年10月30日(水)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 118号室
鈴木悠平 氏 (Univ. Tokyo)
Amenable minimal Cantor systems of free groups arising from
diagonal actions (JAPANESE)
鈴木悠平 氏 (Univ. Tokyo)
Amenable minimal Cantor systems of free groups arising from
diagonal actions (JAPANESE)
代数学コロキウム
16:40-17:40 数理科学研究科棟(駒場) 002号室
いつもと場所が異なりますのでご注意ください
Pierre Charollois 氏 (パリ第6大学)
Explicit integral cocycles on GLn and special values of p-adic partial zeta functions (ENGLISH)
いつもと場所が異なりますのでご注意ください
Pierre Charollois 氏 (パリ第6大学)
Explicit integral cocycles on GLn and special values of p-adic partial zeta functions (ENGLISH)
[ 講演概要 ]
Building on earlier work by Sczech, we contruct an explicit integral valued cocycle on GLn(Z).
It allows for the detailed analysis of the order of vanishing and of the special value at s=0 of the p-adic partial zeta functions introduced by Pi. Cassou-Noguès and Deligne-Ribet. In particular we recover a result of Wiles (1990) on Gross conjecture.
Another construction, now based on Shintani's method, is shown to lead to a cohomologous cocycle. This is joint work with S. Dasgupta and M. Greenberg.
Building on earlier work by Sczech, we contruct an explicit integral valued cocycle on GLn(Z).
It allows for the detailed analysis of the order of vanishing and of the special value at s=0 of the p-adic partial zeta functions introduced by Pi. Cassou-Noguès and Deligne-Ribet. In particular we recover a result of Wiles (1990) on Gross conjecture.
Another construction, now based on Shintani's method, is shown to lead to a cohomologous cocycle. This is joint work with S. Dasgupta and M. Greenberg.
古典解析セミナー
16:00-17:00 数理科学研究科棟(駒場) 122号室
Jacques Sauloy 氏 (Institute de Mathematiques de Toulouse, Universite Paul Sabatier)
The space of monodromy and Stokes data for q-difference equations (ENGLISH)
Jacques Sauloy 氏 (Institute de Mathematiques de Toulouse, Universite Paul Sabatier)
The space of monodromy and Stokes data for q-difference equations (ENGLISH)
[ 講演概要 ]
Riemann-Hilbert correspondance for fuchsian q-difference equations has been obtained by Sauloy along the lines of Birkhoff and then, for irregular equations, by Ramis, Sauloy and Zhang in terms of q-Stokes operators.
However, these correspondances are not formulated in geometric terms, which makes them little suitable for the study of isomonodromy or "iso-Stokes" deformations. Recently, under the impulse of Ohyama, we started to construct such a geometric description in order to apply it to the famous work of Jimbo-Sakai and then to more recent extensions. I shall describe this work.
Riemann-Hilbert correspondance for fuchsian q-difference equations has been obtained by Sauloy along the lines of Birkhoff and then, for irregular equations, by Ramis, Sauloy and Zhang in terms of q-Stokes operators.
However, these correspondances are not formulated in geometric terms, which makes them little suitable for the study of isomonodromy or "iso-Stokes" deformations. Recently, under the impulse of Ohyama, we started to construct such a geometric description in order to apply it to the famous work of Jimbo-Sakai and then to more recent extensions. I shall describe this work.
2013年10月29日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Daniel Matei 氏 (IMAR, Bucharest)
Fundamental groups of algebraic varieties (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Daniel Matei 氏 (IMAR, Bucharest)
Fundamental groups of algebraic varieties (ENGLISH)
[ 講演概要 ]
We discuss restrictions imposed by the complex
structure on fundamental groups of quasi-projective
algebraic varieties with mild singularities.
We investigate quasi-projectivity of various geometric
classes of finitely presented groups.
We discuss restrictions imposed by the complex
structure on fundamental groups of quasi-projective
algebraic varieties with mild singularities.
We investigate quasi-projectivity of various geometric
classes of finitely presented groups.
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